login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178143 Sum of squares d^2 over the divisors d=2 and/or d=3 of n. 3
0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Period 6: repeat [0, 4, 9, 4, 0, 13]. - Wesley Ivan Hurt, Jul 05 2016

LINKS

Table of n, a(n) for n=1..82.

V. Shevelev,A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function sigma_x(n), arXiv:0903.1743 [math.NT], 2009.

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1).

FORMULA

a(n) = Sum_{d|n, d=2 and/or d=3} d^2.

a(n) = -a(n-1) + a(n-3) + a(n-4) for n>4.

G.f.: x*(4+13*x+13*x^2) / ( (1-x)*(1+x)*(1+x+x^2) ).

a(n+6) = a(n).

a(n) = A010675(n) + A021115(n). [R. J. Mathar, May 28 2010]

a(n) = (1/6)*{15*(n mod 6)-11*[(n+1) mod 6]+6*[(n+2) mod 6]+7*[(n+3) mod 6]-3*[(n+4) mod 6]-2*[(n+5) mod 6]}. [Paolo P. Lava, May 24 2010]

a(n) = 4 * (1 + floor(n/2) - ceiling(n/2)) + 9 * (1 + floor(n/3) - ceiling(n/3)). - Wesley Ivan Hurt, May 20 2013

a(n) = 5 + 2*cos(n*Pi) + 6*cos(2*n*Pi/3). - Wesley Ivan Hurt, Jul 05 2016

EXAMPLE

a(1)=0, a(2)=2^2=4 since 2|2, a(3)=3^2=9 since 3|3, a(4)=2^2=4 since 2|4.

MAPLE

seq(op([0, 4, 9, 4, 0, 13]), n=1..30); # Wesley Ivan Hurt, Jul 05 2016

MATHEMATICA

PadRight[{}, 100, {0, 4, 9, 4, 0, 13}] (* Wesley Ivan Hurt, Jul 05 2016 *)

PROG

(PARI) a(n)=[13, 0, 4, 9, 4, 0][n%6+1] \\ Charles R Greathouse IV, May 21 2013

(MAGMA) &cat [[0, 4, 9, 4, 0, 13]^^20]; // Wesley Ivan Hurt, Jul 05 2016

CROSSREFS

Cf. A010675, A021115, A098002, A178142.

Sequence in context: A217393 A285323 A321219 * A070435 A070516 A143298

Adjacent sequences:  A178140 A178141 A178142 * A178144 A178145 A178146

KEYWORD

nonn,easy,less

AUTHOR

Vladimir Shevelev, May 21 2010

EXTENSIONS

Replaced recurrence by a shorter one; added keyword:less - R. J. Mathar, May 28 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)